Evaluation Of Lateral Load Pattern In Pushover Analysis

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Earthquake Resistant Engineering Structures VI279Evaluation of lateral load pattern inpushover analysisS. I. Javadein1 & R. Taghinezhad21Department of Civil Engineering, Islamic Azad University,Bandar Anzali, Iran2Department of Civil Engineering, Islamic Azad University,Torbat Heydariye, IranAbstractThe objective of this study is to evaluate the performance of the frame structuresfor various load patterns and a variety of natural periods by performing pushoverand nonlinear dynamic time history analyses. 3, 5, 7, 9 and 13-story momentsteel frame structures are used in the analyses and the load distributions forpushover analyses are chosen as triangular, IBC (k 2) and rectangular. Theseframes have five different natural periods. Even though the nonlinear dynamictime history analysis is the best way to compute seismic demands, FEMA-356and ATC-40 proposes tthe use of nonlinear static procedure or pushoveranalysis. The five frame structures have been analyzed using the nonlinearprogram SAP2000. This paper is also intended to compare the results ofpushover and nonlinear dynamic time history analyses. To evaluate the resultsfrom the pushover analyses for three load patterns and also five natural periods,nonlinear dynamic time history analyses are performed. Earthquake groundmotions recorded at 3 stations during various earthquakes are used in theanalyses. The ground motion records used in this study include TABAS,NAGHAN and ELCENTRO. Pushover and nonlinear time history analysesresults are compared to choose the best load distribution for a specific naturalperiod for this type of frame structure.Keywords: pushover analysis, nonlinear time history, load patterns, momentresisting frame.WIT Transactions on The Built Environment, Vol 93, 2007 WIT Presswww.witpress.com, ISSN 1743-3509 (on-line)doi:10.2495/ERES070271

280 Earthquake Resistant Engineering Structures VI1IntroductionOnly the life safety and collapse prevention in general earthquake resistantdesign phenomena are explicitly prevented in seismic design codes. The designis generally based on evaluating the seismic performance of structures. It isrequired to consider inelastic behavior while evaluating the seismic demands atlow performance levels. FEMA-356 [1] and ATC-40 [2] use pushover analysisas nonlinear static analysis but nonlinear time history analysis has more accurateresults on computing seismic demands. The purposes in earthquake-resistancedesign are:(a) to prevent non-structural damage in minor earthquakes, which may occurfrequently in life time.(b) to prevent structural damage and minimize non-structural damage inmoderate earthquakes which may occur occasionally.(c) to prevent collapsing or serious damage in major earthquakes which mayoccur rarely. Designs are explicitly done only under the third condition.The objective of this study is to evaluate the performance of the framestructures for various load patterns and variety of natural periods by performingpushover and nonlinear dynamic time history analyses. 3, 5, 7, 9 and 13-storymoment steel frame structures are used in the analyses and the load distributionsfor pushover analyses are chosen as triangular (IBC, k 1), (IBC, k 2) andrectangular, where k is the an exponent related to the structure period to definevertical distribution factor IBC [3]. The five frame structures have been analyzedusing nonlinear program SAP2000 [4] and the results have been compared byrecorded response data. Both nonlinear static pushover analysis and nonlineardynamic time history analysis are performed. The correlations between thesenonlinear analyses are studied. The performance of the buildings subjected tovarious representative earthquake ground motions is examined. Finally, pushoverand nonlinear time history analyses results are compared to choose the best loaddistribution (pattern) for specific natural period for these types of steel momentframe structures.2Ground motion dataThe nonlinear response of structures is very sensitive to the structural modelingand ground motion characteristics. Therefore, a set of representative groundmotion records that accounts for uncertainties and differences in severity,frequency and duration characteristics has to be used to predict the possibledeformation modes of the structures for seismic performance evaluationpurposes. For this study, it is considered as 3 different data used in the nonlineardynamic time history analyses, given in the Table 1. The peak groundaccelerations are in the range 0.348 to 0.722g, where g is acceleration due togravity.WIT Transactions on The Built Environment, Vol 93, 2007 WIT Presswww.witpress.com, ISSN 1743-3509 (on-line)

Earthquake Resistant Engineering Structures VITable 1:Ground motion data used in the 25.0453.8Pga0.722g0.933g0.348gDescription of the frame structureFour steel moment frames with 3, 5, 7, 9 and 13-story were utilized to cover abroad range of fundamental periods. The moment steel frame structures areshown in Figure 1. The case study frames were designed for the AISC-ASD2001[5] and Iranian 2800 Code-ver.3 [6]. Two dimensional models of case studyframes were prepared using SAP2000 considering the necessary geometric andstrength characteristics of all members that affect the nonlinear seismic response.Rigid floor diaphragms were assigned at each story level and the seismic mass ofthe frames were lumped at the mass center of each story. Gravity loadsconsisting of dead loads and 25% of live loads were considered in pushover andnonlinear time history analyses. The columns are assumed as fixed on theground. Yield strength of the steel reinforcements is 2400 kg / cm 2 . Also thecross section of all beams and columns in these frames are IPE and IPB-shapesrespectively. Tree vibration analyses were performed to determine elastic periodsand mode shapes of the frames. The dynamic properties of the case study framesare summarized in Table 2.Sap length in allstructures 4mStory height in 3.2mDL 3200kg/mLL 800Kkg/mFigure 1:Diagram of analyzed 3, 5, 7, 9 and 13-story moment steel frames.WIT Transactions on The Built Environment, Vol 93, 2007 WIT Presswww.witpress.com, ISSN 1743-3509 (on-line)

282 Earthquake Resistant Engineering Structures VIThe first, second and third natural periods of the structures are given inTable 2.Table 2:Dynamic properties of case study frames.Frame3 Story5 Story7 Story9 Story13 Story4T11.071.341.572.582.98Period Nonlinear static pushover analysis of frame structuresThe static pushover procedure has been presented and developed over the pasttwenty years by various researches. The method is also described andrecommended as a tool for design and assessment purpose for the seismicrehabilitation of existing building and represents a main component of theSpectrum Capacity Analysis Method (ATC-40) [2]. It is clear from recentdiscussion that this approach is likely to be recommended in future codes.For low performance levels, to estimate the demands, it is required toconsider inelastic behavior of the structure. Pushover analysis is used to identifythe seismic hazards, selection of the performance levels and design performanceobjectives. In pushover analysis, applying lateral loads in patterns that representapproximately the relative inertial forces generated at each floor level andpushing the structure under lateral loads to displacements that are larger than themaximum displacements expected in design earthquakes (Li [7]). The pushoveranalysis provides a shear vs. displacement relationship and indicates the inelasticlimit as well as lateral load capacity of the structure. The changes in slope of thiscurve give an indication of yielding of various structural elements. The main aimof the pushover analysis is to determine member forces and global and localdeformation capacity of a structure. The information can be used to assess theintegrity of the structure. After designing and detailing the moment steel framestructures, a nonlinear pushover analysis is carried out for evaluating thestructural seismic response. For this purpose the computer program SAP2000 hasbeen used. Three simplified loading patterns; triangular (IBC, k 1), IBC (k 2)and rectangular, where k is an exponent related to the structure period to definevertical distribution factor, are used in the nonlinear static pushover analysis of3, 5, 7, 9 and 13-story steel frame structures. Load criteria are based on thedistribution of inertial forces of design parameters. The simplified loadingpatterns as uniform distribution, triangular distribution and IBC distribution.These loading patterns are the most common loading parameters. Verticaldistribution of seismic forces:WIT Transactions on The Built Environment, Vol 93, 2007 WIT Presswww.witpress.com, ISSN 1743-3509 (on-line)

Earthquake Resistant Engineering Structures VIFx CvxVCvx wx hxkn 283(1)(2)wi hiki 1Cvx Vertical distribution factor.V Total design lateral force or shear at the base of structure.wi and wx The portion of the total gravity load of the structure hi.hx The height from the base.k An exponent related to the structure period.In addition these lateral loadings, frames are subjected live loads and deadweights. P- effects have been taken into the account during the pushoveranalyses. The lateral force is increased for 3, 5, 7, 9 and 13-story steel framesuntil the structures collapsed. Beam and column elements are used to analyze theframes. The beams are assumed to be rigid in the horizontal plane. Inelasticeffects are assigned to plastic hinges at member ends. Strain-hardening isneglected in all elements. Bilinear moment-rotation relationship is assumed forboth beam and column members. The results of the pushover analyses in 3, 5, 7,9 and 13-story steel frames are presented in Figures 2 and 3 respectively.Figure 2:Pushover curves of 3 and 5-story steel frame for three different loadpatterns.WIT Transactions on The Built Environment, Vol 93, 2007 WIT Presswww.witpress.com, ISSN 1743-3509 (on-line)

284 Earthquake Resistant Engineering Structures VIFigure 3:Pushover curves of 7, 9 and 13-story steel frame for three differentload patterns.The pushover curves are shown for three distributions, and for each framestructures. The curves represent base shear-weight ratio versus story leveldisplacements for uniform, triangular and IBC load distribution. Shear V wascalculated by summing all applied lateral loads above the ground level, and theweight of the building W is the summation of the weights of all floors. Besidethese, these curves represent the lost of lateral load resisting capacity and shearfailures of a column at the displacement level. The changes in slope of thesecurves give an indication of yielding of various structural elements, first yieldingof beam, first yielding of column and shear failure in the members. By theincrease in the height of the frame structures, first yielding and shear failure ofthe columns is experienced at a larger roof displacements and rectangulardistribution always give the higher base shear-weight ratio comparing to otherload distributions for the corresponding story displacement (horizontaldisplacement).WIT Transactions on The Built Environment, Vol 93, 2007 WIT Presswww.witpress.com, ISSN 1743-3509 (on-line)

Earthquake Resistant Engineering Structures VI5285Nonlinear dynamic time history analysis of framestructuresAfter performing pushover analyses, nonlinear dynamic time history analyseshave been employed to the five different story frame structures. These frames aresubjected live and dead weights. Also P- effects are under consideration as inpushover analysis. For time history analysis P- effects have been taken into theaccount. Finite element procedure is employed for the modeling of the structuresduring the nonlinear dynamic time history analyses. SAP2000 has been used fornonlinear time history analysis and modeling. The model described for pushoveranalyses has been used for the time history analyses. Mass is assumed to belumped at the joints. The frames are subjected to 3 earthquake ground motions,which are recorded during TABAS, NAGHAN and ELSENTRO for thenonlinear dynamic time history analyses (Figure 4).D 7 % 6 E 1 * 1 F (/&(1752 Figure 4:Acceleration-time histories of ground motion records.These data are from different site classes as I, II, III and IV. The selectedearthquake ground motions have different frequency contents and peak groundaccelerations. The ground motion data are chosen from near-field region toevaluate the response of the frame structures in this region and comparison ofthem with pushover analyses results.The results of nonlinear time history analysis for 3, 5, 7, 9 and 13-story steelframe structure are presented in Figure 5.WIT Transactions on The Built Environment, Vol 93, 2007 WIT Presswww.witpress.com, ISSN 1743-3509 (on-line)

286 Earthquake Resistant Engineering Structures VIFigure 5:Pushover and nonlinear time history results of 3, 5, 7, 9 and13-story.Pushover and nonlinear time history analyses results are compared to forspecific natural period for five different frame structures and for each loaddistributions; rectangular, triangular and IBC (k 2).6ConclusionAfter designing and detailing the moment steel frame structures, a nonlinearpushover analysis and nonlinear dynamic time history analysis are carried out forevaluating the structural seismic response for the acceptance of load distributionfor inelastic behavior. It is assumed for pushover analysis that seismic demandsat the target displacement are approximately maximum seismic demands duringthe earthquake. According to Figures 2 and 3, for higher story frame structures,first yielding and shear failure of the columns is experienced at the larger storydisplacements and rectangular distribution always give the higher base shearweight ratio comparing to other load distributions for the corresponding storydisplacement. As it is presented in Figure 5, nonlinear static pushover analysesfor IBC (k 2), rectangular, and triangular load distribution and nonlinear timehistory analyses results for the chosen ground motion data (all of them are nearfield data) are compared. Pushover curves do not match with nonlinear dynamictime history analysis results especially for higher story moment steel framestructures (9 and 13-story frame structures). The pushover analyses results forWIT Transactions on The Built Environment, Vol 93, 2007 WIT Presswww.witpress.com, ISSN 1743-3509 (on-line)

Earthquake Resistant Engineering Structures VI287rectangular load distribution estimate maximum seismic demands during thegiven earthquakes more reasonable than the other load distributions, IBC (k 2),and triangular.References[1] FEMA (2000b). “Prestandard and Commentary for the SeismicRehabilitation of Buildings”, Report FEMA-356, Federal EmergencyManagement Agency, Washington, DC, U.S.A.[2] ATC-40, “Seismic evaluation and Retrofit of Concrete Buildings”, Vol.1,Applied Technology Council, Redwood City, CA, 1996.[3] IBC, International Building Code, International Conference of BuildingOfficials, Whittier, California, 2000.[4] Computers and Structures Inc. (CSI), SAP2000 Three Dimensional Staticand Dynamic Finite Element Analysis and Design of Structures V7.40N,Berkeley, California.[5] AISC, Manual of Steel Construction: Load and Resistance Factor Design,3rd Edition, American Institute of Steel Construction, Chicago, IL, 2001.[6] Iranian Code of Practice for Seismic Resistant Design of Building, StandardNo. 2800-5, 3rd Edition, Building and Housing Research Center, 2005.[7] Li, Y.R. Non-Linear Time History And Pushover Analyses for SeismicDesign and Evaluation. PhD Thesis, University of Texas, Austin, TX. 1996.WIT Transactions on The Built Environment, Vol 93, 2007 WIT Presswww.witpress.com, ISSN 1743-3509 (on-line)

required to consider inelastic behavior while evaluating the seismic demands at low performance levels. FEMA-356 [1] and ATC-40 [2] use pushover analysis as nonlinear static analysis but nonlinear time history analysis has more accurate results on computing seismic demands. The purposes in earthquake-resistance design are: (a) to prevent non-structural damage in minor earthquakes, which may .

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